Pile roast beef on top of mayonnaise. Sprinkle with the crisp-fried onion strips and top with brie cheese. Spread Dijon mustard on the unbuttered sides of the remaining 4 slices of bread and place on top of brie. You should have 4 sandwiches with buttered tops and bottoms.

Preheat panini-grill or griddle. When hot, place sandwiches on panini grill and cook until golden brown on each side. Cut panini sandwiches in half and serve.